The Cantor's First Diagonal Formalized and Extended

TL;DR

This paper formalizes and extends Cantor's first diagonal argument, providing a simple closed-form bijection between multi-dimensional natural number spaces and the natural numbers.

Contribution

It introduces a formalization and extension of Cantor's diagonal argument, resulting in a new closed-form expression for bijections between k and .

Findings

Derived a closed-form bijection between k and .

Formalized Cantor's diagonal argument for broader application.

Extended the diagonal argument to higher dimensions.

Abstract

We examinate, formalize and extend the reasoning behind the Cantor's first diagonal argument, obtaining a simple closed-form expression for a bijection between $\mathbb{N}^k$ and $\mathbb{N}$.